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\chapter{Introduction}

Satellite communication systems are designed to provide reliable global coverage using low, medium or geostationary earth orbit satellites. Due to free space path lose, tree or hills shadowing and multipath effects caused by surrounding buildings, these communication systems face bad quality of service. The first two effect cause large scale fading and they mainly influence the line of sight path (LOS) and the last one cause small scale fading. In disaster scenarios satellite communication can offer link to the outside world, where terrestrial communication is not possible.

The primary aim of signal modelling of a channel is to avoid the expensive hardware test for the mobile communication systems. For a particular model to be precisely accurate, it requires to find mathematical description of an experimental data and generating an artificial signal with assumed properties. This is typical scenario where signal received by  the mobile vehicle contains LOS path, scattered, reflected, diffracted and refracted components as shown in Figure ~\ref{fig:Propagation Characteristics of Satellite Communication Channel} on page ~\pageref{fig:Propagation Characteristics of Satellite Communication Channel}.



\begin{figure}[htb]
\centering
\includegraphics[width=\textwidth]{./bilder/fadding_effect}
\caption{Propagation Characteristics of Satellite Communication Channel}
\label{fig:Propagation Characteristics of Satellite Communication Channel}
\end{figure}

From past several years, there are so many approaches proposed to model Land Mobile Satellite (LMS) channel. This approaches are  statistical, deterministic and combination of both statistical and deterministic. Deterministic approach provides very high accuracy, but it uses actual analytic path profiles and very long time spending calculations. Statistical approach is most common for LMS channel modelling. Statistical approach modelling is simpler but due to inaccuracy of some parameters this models may give unreliable results. 

This chapter will present the statistical LMS channel models available for LMS channel modelling.

\section{Statistical LMS Channel Model}


In general statistical modelling is mainly used to model LMS channel. There are many methods proposed for statistical channel modelling like two-state channel model, three-state channel model, etc.
 

\subsection{Three-State Statistical LMS channel model}

Three-state channel model proposed in \cite{threestate}, which describes a propagation channel is terms of three possible states (LOS, moderate shadow and deep shadow). The three state model was originally developed for low margin systems, where direct satellite to user terminal communication is only possible in LOS condition. 


Three-state LMS channel model works on existence of three different rate of change (fast, slow, very slow) in the received signal. If there is no LOS condition means our mobile terminal goes in deep shadowed environment like behind the trees or buildings, it is described as very slow state. If there is very small scale change means slow variations. 

This model uses Loo distribution to describe the signal variations within each state and first order Markov model is used to model state transitions \cite{two-state}. 


The three states of propagation characteristics shown in Figure ~\ref{fig:State Information} on page ~\pageref{fig:State Information} with fast, slow and very slow variations.


\subsection{Versatile Two-State Statistical LMS channel model}

The other approach is versatile two-state LMS channel model proposed in \cite{two-state}. For future LMS applications non LOS conditions require more consideration and this problem is accurately addressed in this two-state channel model. This is the revised model of the previous three state channel model. Instead of three state in previous model, this model only consider two states to describe the propagation characteristics of LMS channel.

The two-state model considers only two states Good and Bad as shown in Figure ~\ref{fig:State Information} on page ~\pageref{fig:State Information}. This states are not required to match the LOS and non LOS conditions. The Loo distribution parameters are used in order to characterise the fading conditions within each states. As shown in Figure ~\ref{fig:State Information}, one entire set of Loo parameters are used to describe the two possible states. In this approach we can use first order Markov model or semi-Markov approach to model state transitions and state durations \cite{two-state}.



\begin{figure}[htb]
\centering
\includegraphics[width=\textwidth]{./bilder/states}
\caption{State Information according to propagation characteristics}
\label{fig:State Information}
\end{figure}

As we can see from Figure ~\ref{fig:State Information}, The good state represents areas with unobstructed view of the satellite (less shadowed or unshadowed) means high received signal power, whereas the bad channel state represents areas where the direct satellite signal is shadowed by obstacles means low received signal power.


For our work we will consider Two-State Markov model because the non-LOS components are necessary and need to model more precisely under deep shadow conditions in Urban environments.



This chapter presents the different channel modelling approaches. In the next section we discuss about the Motivation and Goal of the project.



\section{Motivation and Goal}

We will focus on Two-State Statistical channel model proposed in \cite{two-state}. This model assumes Two State (Good and Bad) Markov channel model (not necessarily matching LOS and Non-LOS conditions). In this approach only one entire set of Loo distribution parameters are used to define the possible states.

For the accuracy of the channel simulators, it should need to change it's channel state as frequently as possible. But for the channel simulator it will increase the computational complexity. The generation of new channel state is computationally expensive. For this reason the change of channel state should be made according to the measured signal change but not at higher rate.  

For this state oriented statistical channel model accuracy, we need to accurately identify state change position and it will depend on stationarity region identification. In this work we will try to discuss the problems related to LMS channel stationarity and also try to find the local stationarity regions.

In this report we will discuss about the correlation structure of the received signal and based on this correlation structures we will define stationary region and state change (signal segmentation).


In the next chapter we will discuss about the Correlation Structure of LMS channel.

